If someone offered you $1 million, you’d probably jump at the offer. But what if they offered you a choice of $1 million or a penny that doubles every day for a month? When a penny doubles for 30 days, you might be surprised how much it yields.
If you double 1 penny every day for 30 days, you would end up with over $5 million. This exponential growth showcases the power of compounding over time.
The Growth of a Penny that Doubles for 30 Days
At the beginning of the month, that million dollars will look pretty good. After all, at the end of seven days, you’d end up with a whopping $0.64 if you took the penny. It would take 15 days to break $100 from your penny doubling.
This is when things get interesting though. On Day 14, you have just $81.92 in your penny-based bank account. But on Day 15, you have $163.84. That’s not just a little bit more money. That could be a car payment.
But don’t spend your earnings yet. In three more days, Day 18, you’ll have more than $1,000 — or $1310.72, to be exact.
You might be wondering, at this point, if taking $1 million upfront may have been a better option. On Day 18, you aren’t anywhere close to that $1 million yet based on your penny doubling every 30 days.
How Much Is 1 Penny a Day Doubled for 20 Days?
Hold out for 20 days, though, and you’ll see your money continuing to grow in tangible ways. On Day 20, when a penny doubles for 30 days, you’ll have $5,242.88 in your bank account. By Day 21, you’ll break $10,000.
How Much Is 1 Penny a Day Doubled for 28 Days?
On Day 28, magic happens. Your $671,088.64 becomes well over $1 million: $1,342,177.28. The next day, you’ll be looking at a growing balance of $2,684,354.56. Taking a penny that doubles clearly looks like the better choice compared to accepting $1 million.
How Much is a Penny That Doubles for 30 Days Compared to $1 Million?
When a penny doubles for 30 days, you’ll end up with $5,368,709.12, compared to just $1 million upfront with this hypothetical offer.
How Much is 1 Cent a Day Doubled for 31 Days?
If you can hold off for one more day without cashing in on that $5.3 million+, you’ll wake up on Day 31 with a very nice surprise and a growing net worth. One penny doubled everyday for 31 days leaves you with $10,737,418.24.
The Power of Compounding
You might be amazed by how quickly your penny can grow into one million dollars. It can reach five million dollars and, then finally, on day 31, more than $10.7 million. But that’s how compound growth works.
When you think about saving money, you might think about your money adding up. That is, if you save a penny per day, at the end of the month you’ll have 30 cents. That’s not impressive.
But when money compounds, the money you earn is put back into your savings, and you earn money on that money, too.
Compound Interest v. Simple Interest
Most banks offer compound interest rather than simple interest. If your money is only earning simple interest, you would only earn interest on the principle.
If you had $1,000 in your savings account at 5% interest for a year, you’d earn $50. At the end of the year, you’d have $1,050. At the end of two years, you’d have $1,100 ($1,000 + $50 + $50).
But, if that same $1,000 was earning compound interest, at the end of one year you’d have $1,050 and after two years, you’ll have $1,102.50. That’s because you will earn interest on the $1,050 in your account at the end of year one, not just the principal balance of $1,000.
Most banks that offer compound interest calculate the compound interest daily or monthly, which can help your money grow even faster.
How To Calculate Compound Interest
Calculating compound interest can get confusing. First, you need to know the annual interest rate, how many times the interest is compounded per year, how long (in years) the principal amount stays in your account.
The formula is: A = P (1 + r/n) (nt).
Don’t get overwhelmed by the formula, though. You can just use a compound interest calculator to figure out how fast your money can grow. The U.S. Securities and Exchange Commission provides one at Investor.gov.
Why Would People Still Take $1 Million Instead of a Penny That Doubles?
When you pondered the question of receiving $1 million vs. a penny that doubles for 30 days, did you instinctively say you’d prefer the penny? Most people would.
Maybe you need to make money fast and don’t want to wait 30 days. You would sacrifice more than $5 million dollars in a month for $1 million today. Of course, you could invest that money so it earns compound interest, but it’s highly unlikely you’ll find an investment or savings account where your money would double daily.
For many people who choose $1 million over the penny that doubles, it might be that they cannot easily comprehend how a single penny can grow into more than $5 million in a month–and more than $10 million in 31 days. It might be simple to understand the concept of compounding, but it also sounds too good to be true.
Or maybe, people are afraid that if they don’t take the money upfront, they will lose the penny and all its potential future earnings.
Shift Your Mindset to Let Your Investment Grow
The same thing often happens when people begin investing in the stock market. As your stock’s value goes up, the money you earn is compounded. But you may not believe how much it has the potential to grow over time.
The stock market delivers an average annual return of 10%, and has since 1960. But if you watch the value of your stocks fall in the short term, you may be tempted to pull your money out before it has a chance to grow at that rate.
Trust in the power of compounding and let your money sit over time. You will be pleased to see the returns.